Which recieves the more interest per annum:$150 invested at 4% or $180 invested at 3 1/2%? What is the annual difference​

The equation of the line parallel to 3x-6y=3 and passes through (-2, 3) is y = 1 / 2 x + 4

The equation of the line passes through (-2, 3) and it is parallel to the equation 3x - 6y = 3.

Therefore, the equation of a line can be represented as follows:

y = mx + b

where

Parallel lines have the same slope.

Hence,

3x - 6y = 3

3x - 3 = 6y

y = 1 / 2 x - 1 / 2

Therefore, the slope of the equation is 1 / 2.

Let's find the y-intercept using (-2, 3).

3 = 1 / 2 (-2) + b

3 + 1 = b

b = 4

Therefore, the equation is y = 1 / 2 x + 4

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The image of the function f(x) = x , after the translation is g(x) = x -2 .

In the question

it is given that

the function f(x) = x ,

and f(x) has to be translated 2 units to the right means subtract 2 from the function .

which means g(x) = f(x) - 2

substituting f(x) = x , we get

g(x) = x - 2

the answer in the form of mx+b is g(x) = x - 2

(can refer to the graph given below)

Therefore , The image of the function f(x) = x , after the translation is g(x) = x - 2 .

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10 pounds of food each chicken eat last week.

This is a problem from an algebraic equation. We can solve this problem by following a few steps.

Each chicken eats the same amount of food, as per the question. Let's assume there is x number of chickens.

Therefore, if each chicken eats the same amount of food then the total food required for all chickens is, (x × x) = x² pound.

Again, Mrs. Rollins bought 100 pounds of chicken food.

Hence x² is equivalent to 100 pounds. We can generate an equation from this. Which is,

x² = 100

Or, √x² = √100         [ root both sides ]

Or, x = 10

Now, we can conclude that there are 10 chickens and each chicken eats 10 pounds of food in a week.

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The sum of the internal angles of a triangle is 180°

Since AD is parallel to BC and DC is parallel to AB, the angle ADC must be equal to the angle ABC, which is 123°

Then, the angle CAB is 180° - 24° - 123° = 33°

Question Should look like

determine the distance between (-4,-7) and (-8,-13)

A. [tex]\sqrt{10}[/tex]

B. [tex]\sqrt{82}[/tex]

C. [tex]\sqrt{544}[/tex]

D. [tex]\sqrt{52}[/tex]

Answer: D. [tex]\sqrt{52}[/tex]

Step-by-step explanation:

[tex]a^{2}+b^{2}= c^{2}[/tex]

a =(8-4)... b=(13-7)

a=4, b=6

therefore...

[tex]a^{2}+b^{2}= c^{2}\\4^{2}+6^{2}=c^{2}\\16+36=c^{2}\\52=c^{2}\\c=\sqrt{52}[/tex]

Answer:

⚠️⚠️⚠️⚠️⚠️⚠️♀️

Step-by-step explanation:

⚠️⚠️⚠️♀️

Answer:

7cd(ab-3be+2ef)

Step-by-step explanation:

they all have the number 7 In common so you take that out and you take out whatever letters they have in common

Answer:

7cd(ab - 3be + 2ef

Step-by-step explanation:

Simplify:

    7abcd = 7 * a * b* c * d

  21bcde = 7 * 3 * b * c * d * e

   14cdef = 7 * 2 * c * d * e * f

GCF = 7 cd

7abcd - 21bcde + 14cdef = 7cd*( ab  - 3be + 2ef)

The x- and y-intercepts of the graph of x + y = 18 both have the values of 18

The x-intercept of the function is the point or points where the graph of the function crosses the x-axis i.e. the point where the function equals 0

The equation of the graph is given as

x + y = 18

To calculate the x-intercept, we set the value of y to 0

This is represented as

y = 0

So, we have the following equation

x + 0 = 18

Evaluate the like terms

x = 18

To calculate the y-intercept, we set the value of x to 0

This is represented as

x = 0

So, we have the following equation

0 + y = 18

Evaluate the like terms

y = 18

This means that the x-intercept has a value of 18 and the y-intercept has a value of 18

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The measure of x, m∠DEG, m∠GEF  and m∠DEF will be 5,112°,68°and 180° respectively.

When two lines or rays converge at the same point, the measurement between them is called an "Angle."

It is given that,

m∠DEG = (23x-3)°

m∠GEF = (12x+8)°

As m∠DEF is a straight angle its angle measurement is 180

As a result,

m∠DEF=m∠DEG+m∠GEF

180°=m∠DEG+m∠GEF

Put the given values

180°=(23x-3)°+(12x+8)°

180=35x+5

35x=180-5

35x=175

x=5

Substitute the value of x to obtain all the angles as

m∠DEG=(23x-3)°

m∠DEG=(23(5)-3)°

m∠DEG=112°

For m∠GEF,

m∠GEF=(12x+8)°

substitute the value of x

m∠GEF=(12(5)+8)°

m∠GEF=68°

Thus, the measure of x, m∠DEG, m∠GEF  and m∠DEF will be 5,112°,68°and 180° respectively.

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Reason:

GCF = greatest common factor

LCM = lowest common multiple

GCF of 6 and 8 = 2

LCM of 6 and 8 = (6*8)/GCF = (6*8)/2 = 48/2 = 24

We can list out the multiples of each to confirm this

If Mason's tower is 24 cm tall, then he uses 24/6 = 4 blocks; while Daisy will use 24/8 = 3 blocks for her tower of the same height.

The smallest height that their towers could be 24 cm.

The lowest of two or more natural numbers' common multiples is referred to as the Lowest Common Multiple (LCM). The least Common Multiple and Least Common Divisor are other names for it (LCD). For instance, 12 is the least frequent multiple of 4 and 6.

GCF = greatest common factor

LCM = lowest common multiple

GCF of 6 and 8 = 2

LCM of 6 and 8 = (6*8)/GCF = (6*8)/2 = 48/2 = 24

We can list out the multiples of each to confirm this

multiples of 6 are 6, 12, 18, 24, 30, ...

multiples of 8 are: 8, 16, 24, 32, ...

If Mason's tower is 24 cm tall, then he uses 24/6 = 4 blocks; while Daisy will use 24/8 = 3 blocks for her tower of the same height.

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Answer:

12.56$

Step-by-step explanation:

12 / 3=4

4 × 3.14 = 12.56

Answer:

2x=108

Step-by-step explanation: This is the equation because when it says twice a number, you are multiplying a number two times. In this case, the number is not given, so x is the variable being multiplied two times. If the number was 8, it would look like this: 2(8)=108. Of course this isn't true, but to find the actual answer you would divide two on both sides of the equation. This is so that both of the two's cancel out on the left side of the equation. and the variable is left on that side. Our goal is to isolate the variable. In these types of equations, our goal is to isolate the variable and find what the variable is worth. If we do 108 divided by 2 that gives us 54. Since there was x left on the left side of the equation and there is 108 left on the right side we have our equation. x=54

Number explanation below

2x=108

2x/2=108/2

x=54

Vertex is a common endpoint that is shared by the two rays. Therefore, option B is the correct answer.

We need to define the angle.

An angle is formed when two straight lines or rays meet at a common endpoint. The common point of contact is called the vertex of an angle.

Parts of an Angle

There are two main parts related to an angle - the arms and the vertex.

Arms of the Angle

The two rays which join at a common point to form the angle are called the arms of the angle.

Vertex of the angle

Vertex is a common endpoint that is shared by the two rays.

Vertex is a common endpoint that is shared by the two rays. Therefore, option B is the correct answer.

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Answer: -11

Step-by-step explanation:

The domain of the relation as given in the task content; (x,y): y = x(x-3) / (x+4)(x-7) is the set of all real number values except; -4 and 7 and hence is represented as; { x : x R, x ≠ -4, x ≠ 7}.

It follows from the task content that the domain of the relation given in the task content be determined.

On this note, since the domain of a relation or function simply refers to the set of all possible input values of such function.

Since the relation in this scenario is a rational function, it follows that the domain is the set of all real number values except that which renders the relation undefined.

Therefore, since the values which render the relation undefined, render the denominator equal to 0; we have;

(x+4)(x-7) = 0.

x = -4 OR x = 7.

Ultimately, the domain of the relation is the set of all real numbers except; x = -4 and x = 7.

Therefore, when represented by set builder notation; we have; { x : x R, x ≠ -4, x ≠ 7}.

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If there is no solution to a compound inequality, it can involve AND.

A sentence having two inequality statements connected by the words "or" or "and" is referred to as a compound inequality. The conjunction "and" denotes the equal validity of both statements in the compound sentence. The conjunction "or" means that the entire compound sentence is true as long as either of the two statements is true.

The term "OR" can help us find more solutions, whereas the phrase "AND" can help us find less solutions. As a result, we can create a compound inequality with no solution by using "AND."

Therefore, if there is no solution in compound inequality, it may involve AND.

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The given percentage cannot be represented on the grid.

What is percentage?

A percentage (from Latin: per centum, "by a hundred") is a quantity or ratio stated as a fraction of 100 in mathematics. The percent symbol, "%," is commonly used, however the abbreviations "pct.", "pct," and sometimes "pc" are also used. A % is a non - dimensional (pure) quantity; it does not have a unit of measurement. In the context of sports statistics, the term "%" is frequently used incorrectly since the referred figure is stated as a decimal proportion, not a percentage. Similarly, a team's winning percentage, or the fraction of matches won, is commonly reported as a decimal proportion; a team with a.500 winning percentage has won 50% of its matches.

The given percentage cannot be represented on the grid.

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Answer:

Step-by-step explanation:

After using substitution method - The new height of the painting will be 247cm.

What is the substitution method?

To solve many simultaneous linear equations, use the substitution method in algebra. As implied by the name, this strategy involves replacing a variable's value from one equation with another.

we are given the original width of the painting to be 6cm and the original height to be 19cm.

after enlarging the size of the painting the new and enlarged width becomes 78cm

and we assume the new and enlarged height of the painting to be xcm.

we now the ratios

original height : original width = enlarged height : enlarged width ,

will remain equal,

Hence substituting the numerical values in the ratios we get

19/6 = x/78

19 * 78 = 6x

1482/6 = x

247cm =x

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Based on the weight of the plastic to the weight of the paper, the ratio of plastic to paper in the simplest form is 6 : 1

To find the ratio of plastic to paper, there is a need to convert the weights such that they have the same units.

Assuming we convert the plastics to grams, the number of grams of plastic would be:

= 3 kg x 1,000 grams per kg

= 3,000 grams

The ratio then would be:

3,000 grams of plastic   : 500 grams of paper

To get to the simplest form, divide both sides by 500:

3,000 / 500 : 500 / 500

6 : 1

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From the question, we have:

P(n) = P(n - 1) + n²

P1 = Po + 1² = 0 + 1 = 1

P2 = P1 + 2² = 1 + 4 = 5 (This is option C)

P3 = P2 + 3² = 5 + 9 = 14 (This is option B)

P4 = P3 + 4² = 14 + 16 = 30 (This is option D)

Therefore the number of snowballs cannot be 25.

So, the correct option is A, which is 25.

Answer:

the answer is A

Step-by-step explanation:

To check your answer, move 4 units to the right and 3 units up

The value of x are 4 and 2.4 after simplifying and applying the quadratic formula.

Any equation of the form [tex]\rm ax^2+bx+c=0[/tex] where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.

As we know, the formula for the roots of the quadratic equation is given by:

[tex]\rm x = \dfrac{-b \pm\sqrt{b^2-4ac}}{2a}[/tex]

The equation is:

4/(x - 2) + 3/(x - 3) = 5

4(x - 3) + 3(x - 2) = 5(x -2)(x - 3)

4x - 12 + 3x - 6 = 5x² - 25x + 30

5x² - 32x + 48 = 0

After solving the above quadratic equation by the formula:

[tex]\rm x = \dfrac{-(-32) \pm\sqrt{(-32)^2-4(5)(48)}}{2(5)}[/tex]

x = 4

x = 2.4

Thus, the value of x are 4 and 2.4 after simplifying and applying the quadratic formula.

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The quadratic function that models the path of the second kick is given by:

y = -2/125(x - 25)² + 10.

The equation of a quadratic function, of vertex (h,k), is given by the following rule:

y = a(x - h)² + k

In which the coefficients are explained as follows:

For the first kick, the equation is:

y = -1/40(x - 25)² + 15.

Meaning that the ball reached a maximum height of yards after an horizontal distance of 25 yards.

For the second kick, the horizontal distance is the same, but the maximum height if 5 yards less, that is, of 10 yards, hence the vertex is:

(h,k) = (25, 10).

Hence the equation is:

y = a(x - 25)² + 10.

After 50 yards, the ball hits the ground, hence the leading coefficient a is found as follows:

0 = a(50 - 25)² + 10

625a = -10

a = -10/625

a = -2/125

Hence:

y = -2/125(x - 25)² + 10.

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We can conclude that the mode of the following data are 4 and 5.

As the given data set is:

Mode is calculated when in the given data set the number appears most often.

So, count each number as we get the result:

Therefore, the modes are 4 and 5.

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If one angle of a 3-sided triangle measures 115° and the other two angles measure "x" degrees each, then the equation to be solved to obtain the value of "x" is [(115 + 2x) = 180] and the value of "x" will be 32.5°.

As per the question statement, one angle of a 3-sided triangle measures 115° and the other two angles measure "x" degrees each.

We are required to determine a Linear equation of singular value that can describe our concerned situation, and solving which, we will be able to obtain our desired value of "x".

To solve this question, we need to know about one basic yet very important property of a triangle, that is, the sum of all the three interior angles of a triangle is equal to 180 degrees.

Here, the three angles measure 115°, x° and x°.

Therefore, our required equation will [(115 + x + x)° = 180°]

                                                         or, [(115 + 2x)° = 180°]

Now solving the above mentioned equation to obtain the value of "x", we get, [(115 + 2x)° = 180°]

Or, [2x = (180 - 115)°]

Or, (2x = 65°)

Or, x = (65/2)°

or, x = 32.5°

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By solving a quadratic equation, we will see that the necklace hits the ground 2 seconds after it is dropped.

We know that the function:

f(t) = 16*t^2

Represents the distance that an object falls down in t seconds.

If the necklace is dropped from a height of 64 feet, the necklace will hit the ground when the distance that an object falls down in t seconds is equal to 64 feet, so we just need to solve the quadratic equation:

f(t) = 64

16*t^2 = 64

t^2 = 64/16 = 4

t = √4 = 2

The necklace will hit the ground after 2 seconds.

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Answer: -19/8

What is an improper fraction?

  An improper fraction is where the numerator is greater than the denominator. To turn -2 3/8 into an improper fraction, we will "combine" -2 and 3/8.

First, we will find what -2 becomes. -2 is the same as two wholes:

     -2 * 8 = -16

Next, we will subtract this into the numerator of the fraction:

     -16 - 3 = -19

Lastly, we will put this new numerator over the denominator:

     -2 3/8 = -19/8

Answer:

y = 4x -80

Step-by-step explanation:

We need the slope and the y intercept.

The y intercept is -80.  This is where the line crosses the y axis.

The slope is the change in y over the change in x.  

Let's go from point (0,-80) the y intercept the the point that cross the x axis (20,0)  Start at -80, how many units to you go up until you are at the same level as point (20,0)? 80 units.  Now, from (0,0) how many units do you go right to get to (20,0)? 20.

We end up go 80 unit up and 20 units right, this would be written [tex]\frac{80}{20}[/tex] Which simplifies to 4.  This is our slope.

Slope (m) = 4

y intercept (b)= -80  Plug those into

y = mx + b

y = 4x -80

Explanation.

The question asked us to write the equation of the line that passes through the points (2,8) and (-2,10)

To do this, we can use the formula:

In our case, we have

We will simply put all the values above into the formula to get the equation of the line

Simplifying further

Cross multiplying

Therefore, the equation of the line is